April  2010, 6(2): 363-380. doi: 10.3934/jimo.2010.6.363

Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones

1. 

Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China

Received  April 2009 Revised  December 2009 Published  March 2010

Based on the KK smoothing function, we introduce a regularized one-parametric class of smoothing functions and show that it is coercive under suitable assumptions. By making use of the introduced regularized one-parametric class of smoothing functions, we investigate a smoothing Newton algorithm for solving the generalized complementarity problems over symmetric cones (GSCCP), where a nonmonotone line search scheme is used. We show that the algorithm is globally and locally superlinearly convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis.
Citation: Xiao-Hong Liu, Wei-Zhe Gu. Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones. Journal of Industrial & Management Optimization, 2010, 6 (2) : 363-380. doi: 10.3934/jimo.2010.6.363
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